We refer to the two considered flavor “toy models" we consider as model 1 and model 2. They have been discussed in the context of SUSY GUTs in [1]}, [2]}. We assume for both models single operator dominance in each entry [3]}, [2]}, [5]}, [6]}, [7]}, including now also the first family of quarks and leptons.
For the neutrino sector in model 1 and model 2 we choose the CSD2 [8]}, [9]} and CSD3 [10]} texture, respectively. Moreover, we assume that the added scalar fields with intermediate-scale masses \(\Phi _8\) , \(\Phi _6\)  and \(\Phi _{(3,3)}\)  only effect the RG evolution of the gauge couplings, but not the running of the SM Yukawa couplings. This is consistent with the assumption of single operator dominance, since, as it will be discussed later, the Higgs representation \(\textbf {45}_H\)  only interacts with the fermionic representations \(\bar{5}_{F2}\bar{5}_{F2}\) , but not with any other fermionic representations. Single operator dominance then implies that the interactions between the intermediate-scale mass fields \(\Phi _8\) , \(\Phi _6\)  and \(\Phi _{(3,3)}\)  and the SM fermions are up to Clebsch-Gordan (CG) factors equal to the 22 entry of the down-quark Yukawa matrix \((\textbf {Y}_d)_{22}\)  which is of the order of \(\mathcal {O}(10^{-4})\) . Hence, their effect on the running of the SM Yukawa couplings is negligible.
